Function distributionPDF

src/compute-engine/library/distributions.ts:263–336

(
  ce: ComputeEngine,
  dist: Expression,
  x: Expression
)

        'distribution, evaluated at x.',
      complexity: 7500,
      signature: '(distribution, number) -> number',
      evaluate: ([dist, x], { numericApproximation, engine: ce }) => {
        if (!dist || !x || !isDistributionExpression(dist)) return undefined;
        const r = distributionPDF(ce, dist, x);
        if (!r) return undefined;
        return numericApproximation ? r.N() : r.evaluate();
      },
    },

    CDF: {
      description:
        'Cumulative distribution function P(X ≤ x) of a distribution.',
      complexity: 7500,
      signature: '(distribution, number) -> number',
      evaluate: ([dist, x], { numericApproximation, engine: ce }) => {
        if (!dist || !x || !isDistributionExpression(dist)) return undefined;
        const r = distributionCDF(ce, dist, x);
        if (!r) return undefined;
        return numericApproximation ? r.N() : r.evaluate();
      },
    },

    Quantile: {
      description:
        'Quantile (inverse CDF): the least x with CDF(x) ≥ p, for p in [0, 1]. ' +
        'The first argument may also be a data collection, in which case the ' +
        'empirical quantile is returned.',
      complexity: 7500,
      signature: '(distribution | collection<any>, number) -> number',
      evaluate: ([dist, p], { numericApproximation, engine: ce }) => {
        if (!dist || !p) return undefined;
        const pv = litVal(p);
        if (pv !== undefined && (pv < 0 || pv > 1))
          return rangeError(ce, '0 ≤ p ≤ 1', p);
        // Empirical quantile of a data collection (distinguished from a
        // distribution by the first argument's shape).
        if (!isDistributionExpression(dist)) {
          if (!dist.isFiniteCollection) return undefined;
          const r = empiricalQuantile(ce, dist, p, pv);
          if (!r) return undefined;
          return numericApproximation ? r.N() : r.evaluate();
        }
        const r = distributionQuantile(ce, dist, p, pv, !!numericApproximation);
        if (!r) return undefined;
        return numericApproximation ? r.N() : r.evaluate();
      },
    },
  },
];

//
// Closed-form lowering. All construction uses `ce.function('Add'|…)` (never the
// `.add()`/`.mul()` methods, which fold exact literal pairs to floats), and no
// handler calls `.simplify()`. The returned expression is evaluated by the
// caller (exact under `evaluate`, float under `.N()`).
//

function distributionPDF(